Most newer saddles tend to be more multipurpose.
The key is to find a saddle that fits the horse and you.
I don't understand the point of your reply. Newer designs use the terms, "all purpose" or general purpose" or "trail saddle" or "pleasure saddle". Those are the terms that makers use to capture a wider range of buyers.
A barrel saddle is still a barrel saddle, a roping saddle is still just that, as is a reining saddle. It is the design of the saddle - the type and material of the tree, the height and shape of the cantle, the placement of the leathers, etc., that dictates it's use. If I walked into a tack shop (or read an ad) that stated "this saddle is a good all around saddle that you can do most anything in", I would think to myself that this person is only trying to sell a saddle, not see to my needs.
You can have a barrel saddle that fits you and your horse to perfection and you still couldn't hold a cow in it. If a saddle is marketed as a barrel saddle, I would expect that to be the purpose of the design, and not to put in a 5 hour trail ride in.
Fit for you and your horse are the most important elements in general but if you don't take into consideration the design of the saddle, you may end up with something that will make you and/or your horse miserable on a long trail ride or break the tree on if you wanted to rope and drag something.